Am I right about that AEAD encryption/decryption uses a TLS sequence number twice, first time in the nonce and a second in additional data?
And why did they make the TLS 1.2 sequence number 2 times bigger than the TSP sequence number? Why does they need this overhead?
About additional data from rfc5246#page-25
The additional authenticated data, which we denote as additional_data, is defined as follows:
additional_data = seq_num + TLSCompressed.type +
TLSCompressed.version + TLSCompressed.length;
About nonce from rfc5288#page-2
struct { opaque salt[4]; opaque nonce_explicit[8]; } GCMNonce;
The salt is the "implicit" part of the nonce and is not sent in the packet. Instead, the salt is generated as part of the handshake process: it is either the client_write_IV (when the client is sending) or the server_write_IV (when the server is sending). The salt length (SecurityParameters.fixed_iv_length) is 4 octets.
The nonce_explicit is the "explicit" part of the nonce. It is chosen by the sender and is carried in each TLS record in the GenericAEADCipher.nonce_explicit field. The nonce_explicit length (SecurityParameters.record_iv_length) is 8 octets.
Each value of the nonce_explicit MUST be distinct for each distinct invocation of the GCM encrypt function for any fixed key. Failure to meet this uniqueness requirement can significantly degrade security. The nonce_explicit MAY be the 64-bit sequence number.